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Workshop 5

*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 07 Dec 2010 13:27:14 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg.htm/, Retrieved Tue, 07 Dec 2010 14:33:04 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Exponential Smoothing

Dataseries X:

» Textbox « » Textfile « » CSV «

-5 -1 -2 -5 -4 -6 -2 -2 -2 -2 2 1 -8 -1 1 -1 2 2 1 -1 -2 -2 -1 -8 -4 -6 -3 -3 -7 -9 -11 -13 -11 -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11 -12 -10 -15 -15 -15 -13 -8 -13 -9 -7 -4 -4 -2 0

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.81736044436888
beta	0.186444348831529
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	-2	3	-5
4	-5	2.15123659910057	-7.15123659910057
5	-4	-1.54565543853273	-2.45434456146727
6	-6	-1.77751676830599	-4.22248323169401
7	-2	-4.09805836763391	2.09805836763391
8	-2	-0.93271147117745	-1.06728852882255
9	-2	-0.517240405753006	-1.48275959424699
10	-2	-0.667320004723815	-1.33267999527618
11	2	-0.897820560089879	2.89782056008988
12	1	2.77112805251206	-1.77112805251206
13	-8	2.3539565885523	-10.3539565885523
14	-1	-6.65634201558679	5.65634201558679
15	1	-1.71847323190129	2.71847323190129
16	-1	1.23237203105538	-2.23237203105538
17	2	-0.203603955094269	2.20360395509427
18	2	2.32202349556383	-0.322023495563832
19	1	2.73422909036914	-1.73422909036914
20	-1	1.72787064417432	-2.72787064417432
21	-2	-0.506357410451018	-1.49364258954898
22	-2	-1.95939580761916	-0.0406041923808396
23	-1	-2.23096585845312	1.23096585845312
24	-8	-1.27561520811459	-6.72438479188541
25	-4	-7.84739753333596	3.84739753333596
26	-6	-5.1919096472845	-0.808090352715497
27	-3	-6.46478010411762	3.46478010411762
28	-3	-3.71716967896299	0.71716967896299
29	-7	-3.10605624103229	-3.89394375896771
30	-9	-6.85729132731534	-2.14270867268466
31	-11	-9.50366829060175	-1.49633170939825
32	-13	-11.8497516266567	-1.15024837334333
33	-11	-14.0882490547168	3.08824905471684
34	-9	-12.3917411633319	3.39174116333187
35	-17	-9.9302958080145	-7.0697041919855
36	-22	-17.0969901053992	-4.90300989460079
37	-25	-23.2398948291037	-1.76010517089627
38	-20	-27.0821399134875	7.08213991348746
39	-24	-22.6178204907380	-1.38217950926195
40	-24	-25.2825343783558	1.28253437835582
41	-22	-25.5737682572523	3.57376825725229
42	-19	-23.4476236597478	4.44762365974783
43	-18	-19.9294409085906	1.92944090859057
44	-17	-18.1754893159959	1.17548931599592
45	-11	-16.8586524871205	5.85865248712049
46	-11	-10.8211701762907	-0.178829823709291
47	-12	-9.74573936657476	-2.25426063342524
48	-10	-10.7102154237735	0.710215423773509
49	-15	-9.14341469720308	-5.85658530279692
50	-15	-13.8365552590952	-1.16344474090476
51	-15	-14.8710083111426	-0.128991688857363
52	-13	-15.0795976887558	2.07959768875584
53	-8	-13.1660589298778	5.16605892987782
54	-13	-7.94250156877353	-5.05749843122647
55	-9	-11.8459990889174	2.84599908891743
56	-7	-8.85578219965196	1.85578219965196
57	-4	-6.39212262843485	2.39212262843485
58	-4	-3.12553869033348	-0.87446130966652
59	-2	-2.66219236555719	0.662192365557194
60	0	-0.84193313483474	0.84193313483474

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.25354316375645	-5.73263452071978	8.23972084823267
62	2.66085662113023	-7.0708168264078	12.3925300686683
63	4.06817007850401	-8.42836093864608	16.5647010956541
64	5.47548353587779	-9.86880042163211	20.8197674933877
65	6.88279699325157	-11.4153906114871	25.1809845979902
66	8.29011045062535	-13.0771556173939	29.6573765186446
67	9.69742390799913	-14.8570692121823	34.2519170281806
68	11.1047373653729	-16.7552662694282	38.964741000174
69	12.5120508227467	-18.7704839699806	43.794585615474
70	13.9193642801205	-20.9007676464047	48.7394962066457
71	15.3266777374943	-23.1438373215584	53.7971927965469
72	16.7339911948680	-25.4972853789358	58.9652677686719

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/10ya81291728431.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/10ya81291728431.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/26m2m1291728431.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/26m2m1291728431.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/36m2m1291728431.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728779yl68l164sx6axsg/36m2m1291728431.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)

if (par2 == 'Single') K <- 1

if (par2 == 'Double') K <- 2

if (par2 == 'Triple') K <- par1

nx <- length(x)

nxmK <- nx - K

x <- ts(x, frequency = par1)

if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)

if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)

fit

myresid <- x - fit$fitted[,'xhat']

bitmap(file='test1.png')

op <- par(mfrow=c(2,1))

plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')

plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')

par(op)

dev.off()

bitmap(file='test2.png')

p <- predict(fit, par1, prediction.interval=TRUE)

np <- length(p[,1])

plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')

spectrum(myresid,main='Residals Periodogram')

cpgram(myresid,main='Residal Cumulative Periodogram')

qqnorm(myresid,main='Residual Normal QQ Plot')

qqline(myresid)

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'Value',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'alpha',header=TRUE)

a<-table.element(a,fit$alpha)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'beta',header=TRUE)

a<-table.element(a,fit$beta)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'gamma',header=TRUE)

a<-table.element(a,fit$gamma)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observed',header=TRUE)

a<-table.element(a,'Fitted',header=TRUE)

a<-table.element(a,'Residuals',header=TRUE)

a<-table.row.end(a)

for (i in 1:nxmK) {

a<-table.row.start(a)

a<-table.element(a,i+K,header=TRUE)

a<-table.element(a,x[i+K])

a<-table.element(a,fit$fitted[i,'xhat'])

a<-table.element(a,myresid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Forecast',header=TRUE)

a<-table.element(a,'95% Lower Bound',header=TRUE)

a<-table.element(a,'95% Upper Bound',header=TRUE)

a<-table.row.end(a)

for (i in 1:np) {

a<-table.row.start(a)

a<-table.element(a,nx+i,header=TRUE)

a<-table.element(a,p[i,'fit'])

a<-table.element(a,p[i,'lwr'])

a<-table.element(a,p[i,'upr'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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